Tuesday, July 30, 2013

Dialectic as the Self-Progression of Self-Activity and of the Resulting Self-Change.

Dear Readers,

I have reproduced, below, F.E.D. Vignette #14, by F.E.D. Chief Public Liaison Officer Aoristos Dyosphainthos.

The link to the F.E.D. website version of this vignette is given below --






F.E.D. Vignette #14 --

Dialectic as Self-Progression of Self-Activity and of Resulting Self-Change

by Aoristos Dyosphainthos

Authors Preface.  The purpose of F.E.D. Vignette #14 is to illustrate the ways in which F.E.D.’s Dyadic Seldon Function captures characteristics that have, at various moments, from antiquity all the way through to modern times, been insightfully ascribed to the universal dialectical process, including especially the characteristics of self-activity”, of self-change, or «auto-kinesis» [Plato], and of [e.g., ‘‘‘dyadic’’’, or second degree] nonlinearity.

A Note about the On-Line Availability of Definitions of F.E.D. Key Technical Terms.  Definitions of Encyclopedia Dialectica technical terms, including of E.D. ‘neologia’, are available on-line via the following URLs --

-- by clicking on the links associated with each such term, listed, in alphabetic order, on the web-pages linked-to above.

Links to definitions of the Encyclopedia Dialectica special terms most fundamental to this vignette are as follows --


«arithmos» and «arithmoi»

Diachronic vs. Synchronic

Dyadic Seldon Function as ‘‘‘Self-Reflexive Function’’’

Dyadic Seldon Function as Self-Iteration



-- and we plan to expand these definitions resources as the Encyclopedia Dialectica  Dictionary Project unfolds.

[Note:  ‘‘‘Arithmetical Quantifiers’’’ vs. ‘Arithmetical Qualifiers’.  In the phrase “3 apples”, we term “3” the “arithmetical [“pure”-]quantifier”, and “apples” the ‘‘‘ontological’’’ -- or kind of thing -- ‘‘‘qualifier’’’.  In the phrase “3 pounds of apples”, we term “pounds” the metrical[-unit] qualifier’ -- or ‘‘‘unit of measure qualifier’’’ -- quantified by the 3, which, together, quanto-qualify the ontological qualifier’, “apples”.  A key use-value of the dialectical arithmetics is to provide algorithmic, ideographical-symbolic systems for the various kinds of ‘arithmetical qualifiers’, both with and without the co-presence of ‘‘‘arithmetical quantifiers’’’.].

I.  Introduction:  The Marxian Provenance of Concepts of Self-Activity and Self-Change.  The key terms for this vignette -- self-activity and self-change -- first emerged, in Marx’s writing, very close to the original irruption of the psychohistorical materialist theory that is now called “Marxian theory”, in what Engels called “the first document in which is deposited the brilliant germ of a new world outlook”, namely, in Marx’s “Theses of Feuerbach”, in the third of his eleven theses, written by Marx in early 1845, on the eve of the continent-wide republican revolutions of 1848 in which both Marx and Engels were to later participate --

The materialistic doctrine concerning the change of circumstances and education forgets that circumstances are changes by men and that the educator must himself be educated.

Hence this doctrine must divide society into two parts -- one of which towers above [Engels: “as in Robert Owens”].”

The coincidence of the change of circumstances and of human activity or self-change can be comprehended and rationally understood only as revolutionary practice.

[Loyd D. Easton and Kurt H. Guddat, editors and translators, Writings of the Young Marx on Philosophy and Society, Doubleday & Company, Inc. [NY:  1967], p. 401, emphasis added by A.D.].

During 1845-1846, Marx and Engels co-authored an extensively-articulated presentation of their new, psychohistorical materialist world outlook, which, however, was not published until 1932, and in which they summarized that new, psychohistorical materialist world outlook as follows --

...reality is only the product of the preceding intercourse of individuals themselves. ... 

The difference between the individual as a person and what is accidental to him is not a conceptual difference but a historical fact. ... 

It is not a distinction that we have to make for each age, but one which each age makes itself from among the different elements which it finds in existence, and indeed not according to any theory, but compelled by material collisions in life.   

What appears accidental to the later age as opposed to the earlier -- and this applies also to the elements handed down by an earlier age -- is a form of intercourse [A.D.:  later, Marx uses the term “social relations of production” in place of his original term, “forms of [human-social] intercourse”.], which corresponded to a definite stage of development of the productive forces.   

The relation of the productive forces to the form of intercourse is the relation of the form of intercourse to the occupation or activity of the individuals. 

(The fundamental form of this activity is, of course, material, on which depend all other forms -- mental, political, religious, etc.  The various shaping of material life is, of course, in every case dependent on the needs which are already developed, and the production, as well as the satisfaction, of these needs is an historical process, which is not found in the case of a sheep or a dog..., although sheep and dogs in their present form certainly, but malgré eux, are products of an historical process.)   

The conditions under which individuals have intercourse with each other ... are conditions appertaining to their individuality, in no way external to them; conditions under which these definite individuals, living under definite relationships, can alone produce their material life and what is connected with it, are thus the conditions of their self-activity and are produced by this self-activity.*  [*[marginal note by Marx:]  Production of the form of intercourse itself.].   

The definite condition under which they produce, thus corresponds, as long as the contradiction has not yet appeared, to the reality of their conditioned nature, their one-sided existence, the one-sided-ness of which only becomes evident when the contradiction enters on the scene and thus exists for the later individuals. 

Then this condition appears as an accidental fetter, and the consciousness that it is a fetter is imputed to the earlier age as well.

These various conditions, which appear first as conditions of self-activity, later as fetters upon it, form in the whole evolution of history a coherent series of forms of intercourse, the coherence of which consists in this:  in the place of an earlier form of intercourse, which has become a fetter, a new one is put, corresponding to the more developed productive forces, and, hence, to the advanced mode of the self-activity of individuals -- a form which in turn becomes a fetter and is then replaced by another.   

Since these conditions correspond at every stage to the simultaneous development of the productive forces, their history is at the same time the history of the evolving productive forces taken over by each new generation, and is, therefore, a history of the development of the forces of the individuals themselves.”

Since this evolution takes place naturally, i.e., is not subordinated to a general plan of freely combined individuals, it proceeds from various localities, tribes, nations, branches of labour, etc., each of which to start with develops independently of the others.   

Furthermore, it takes place only very slowly; the various stages and interests are never completely overcome, but only subordinated to the prevailing interest and trail along beside the latter for centuries afterwards [A.D.:  the latter phenomenon belongs to what F.E.D. terms the evoluteness of meta-evolution, and is captured by the double-«aufheben» evolute product rule of categorial multiplication, which undergirds the Seldon Functions, as we shall see below.].

[Karl Marx, Frederick Engels, The German Ideology, Progress Publishers [Moscow: 1968], pp. 88-90, emphasis added by A.D.]

In the voluminous 1857-1858 work by Marx, posthumously entitled Foundations of the Critique of Political Economy [“«Grundrisse»”], and first published in 1939, in its section entitled “Forms which precede capitalist production. (Concerning the process which precedes the formation of the capital relation or of original accumulation)”, Marx describes the self-change which results from this self-activity of human “social individuals” in the self-development of the early agricultural village communities of humankind -- all the way from gradual, “evolutionary”, quantitatively-“dynamical” self-change, to “sudden”, “revolutionary self-change, or, in F.E.D.’s version, to meta-evolutionary, socio-onto-dynamical, meta-dynamical, meta-finite singularity self-change, in the following terms --

...In so far as property is merely a conscious attitude to the conditions of production as to one’s own -- an attitude established by the community for the individual, proclaimed and guaranteed as law; in so far as the existence of the producer therefore appears as an existence within the objective conditions belonging to him, it is realized only through production.   

Actual appropriation takes place not through the relationship to these conditions as expressed in thought, but through active, real relationship to them; in the process of positing them as the conditions of man’s subjective activity.

But this also clearly means that these conditions change.

What makes a region of the earth into a hunting-ground, is being hunted over by tribes; what turns the soil into a prolongation of the body of the individual is agriculture.   

Once the city of Rome had been built and its surrounding land cultivated by its citizens, the conditions of the community were different from what they had been before. 

The object of all these communities is preservation, i.e., the production of the individuals which constitute them as proprietors, i.e., in the same objective mode of existence, which also forms the relationship of the members to each other, and therefore forms the community itself.   

But this reproduction is at the same time necessarily new production and the destruction of the old form.” ...

... “The act of reproduction itself changes not only the objective conditions -- e.g., transforming village into town, the wilderness into agricultural clearings, etc. -- but the producers change with it, by the emergence of new qualities, by transforming and developing themselves in production, forming new powers and new conceptions, new modes of intercourse, and new speech.” ...

... “The community itself appears as the first great force of production.” ...

...In the last instance the community and the property resting upon it can be reduced to a specific stage in the development of the forces of production of the labouring subjects -- to which correspond specific relations of these subjects with each other and with nature.

 Up to a certain point, reproduction.  Thereafter, it turns into dissolution.” ...

... All the forms in which the community imputes to the subjects a specific objective unity with the conditions of their production, or in which a specific subjective existence imputes the community itself as condition of production, necessarily correspond only to a development of the forces of production which is limited both in fact and in principle.  (These forms are of course more or less [A.D.:  pre-human-]naturally evolved, but at the same time also the results of a [A.D.:  human-]historic process.

The evolution of the forces of production dissolves them, and their dissolution is itself an evolution of the human forces of production.”

Labour is initially undertaken on a certain basis -- first primitive -- then historical.  Later, however, this basis or presupposition is itself cancelled [A.D.:  i.e., becomes «aufheben»] ... as having become too narrow for the development of the progressive human horde.

[E. J. Hobsbawm, ed., Jack Cohen, transl., Karl Marx:  Pre-Capitalist Economic Formations, Internat’l. Publishers [NY:  1969], pp. 92-97, emphasis added by A.D.].

Lastly, in volume one of Marx’s «magnum opus» -- Capital:  A Critique of Political Economy -- we find the following account of human self-activity and self-changeas human self-development in Marx’s definitional description of his core category of human labor --

Labour is, in the first place, a process in which both man and Nature participate, and in which man of his own accord starts, regulates, and controls the material re-actions between himself and Nature.   

He opposes himself to Nature as one of her own forces, setting in motion arms and legs, head and hands, the natural forces of his own body, in order to appropriate Nature’s productions in a form adapted to his own wants.   

By thus acting on the external world and changing it, he at the same time changes his own nature.   

He develops his slumbering powers... .” 

[Karl Marx, Capital, Volume I, International Publishers [New York:  1967], p. 177, emphasis added by A.D.].

II.  E.D. Interpretation of the Initial Generic Ordinal Qualifiers undergirding the Seldon Function NQ_ Arithmetic.  Perhaps a bit surprisingly, upon first apprehension, the first four, first-order-logic, Dedekind-Peano Postulates for the “Natural” Numbers focus on their ordinality, not on their cardinality, viz. --

1.  1 is a “Natural Number”.

2.  The successor of any “Natural Number” is also a “Natural Number”.

3.  No two, distinct “Natural Numbers” have the same successor.   

4.  1 is not the successor of any “Natural Number”, i.e., 1 has no ancestor within the “Natural Numbers”.

These postulates thus identify the essence of the “Natural Numbers”, explicitly, in terms of [apparently purely-]quantitative ordinality.  In keeping with this focus on the ordinal, Seldon defines the system of the NQ_ dialectical arithmetic -- the first antithesis-system, or contra-system, to the “Natural Numbers” as «arché»-system -- in terms of qualitative ordinality.  The NQ , which he also calls the meta-Natural meta-Numbers, are, in their simplest, least-interpreted essence, a consecutive sequence of ‘meta-numeral’ ideograms representing the successive qualities, not the quantities, of ordinality -- the quality of first-ness’, followed by the quality of second-ness’, followed by the quality of third-ness’, and so on... -- satisfying the four first-order-logic contra-Peanic, Qualo-Peanic axioms:  

1q.  The ordinal qualifier for the quality of first-ness’ is an element of the consecuum of generic ordinal qualifiers.

2q.  The successor of any element of the consecuum of generic ordinal qualifiers is also an element of same.

3q.  Any two, distinct ordinal qualifiers have qualitatively unequal successors.   

4q.  The ordinal qualifier for the quality of first-ness’ is «arché»:  not the successor of any element of its consecuum.

The symbols, or meta-numerals, that stand for the meta-numbersof the NQ archéonic consecuum are derived, syntactically, in a way which represents the semantic self-subsumption, self-subordination, or self-demotion [dialectical, self-«aufheben» self-negation] of the “Natural Numbers”.  That derivation is part of the positive fruition of the dialectical, immanent self-critique of the “Natural Numbers”, which divulges the NQ as the implicit, most extreme known opposite, Non-Standard Model” of the “Standard”, Peano “Natural Numbers”.  It involves the turning of the generic ordinal quantifiers of the “Natural Numbers” into the generic ordinal qualifiers of the NQ meta-Natural meta-Numbers.  The conceptual self-subsumptionof the quantitative ordinality intended by the Dedekind-Peano Postulates surfaces the NQ as their hitherto hidden, implicit intra-dual, based upon the generic quality of ordinality, a ‘‘‘genericity’’’ which we represent by the meta-numeralic ideogram ‘q’.  That meta-numeral component represents qualitative ordinality, or ordinal quality, in general:  just ‘q’, or, more fully expressed, just qN.

To fully express, meta-numeral-y, or ideographically, the consecuum of specific ordinal qualities, namely --

NQ   =  {first-ness’; second-ness’; third-ness’, etc.}

-- we must add a second meta-numeral component, via ‘‘‘subordinating’’’ specificNatural Numbers”, as specific ordinal quantifiers, to the generic ordinal qualifier symbol ‘q’, by subscripting those specificNatural Numbers” to a ‘script-level’ ‘q’, ‘‘‘above’’’ them, yielding --

NQ   =  { q1, q2, q3, ... } [in which each meta-number is a minimal, «genos»/«species» «arithmos eidetikos» in its own right], 


N  =  { 1, 2, 3, ... }. 

Note that this opposition of an arithmetical system of purely-quantitative ordinality, based upon the N, versus an arithmetical system of purely-qualitative ordinality, based on the NQ, is not a radical dualism, imagined as an absolute, irreconcilable diremption between an absolute quantitative and an absolute qualitative.  This opposition is, on the contrary, a dialectical antithesis-sum.  The N quantifiers are still there, as specifiers -- still present -- in, or ‘‘‘under’’’, the generic qs of the NQ qualifiers, though subsumed, subordinated, demoted -- demoted to being their mere subscripts or denominators:  The N quantifiers are still contained in[side] [‘‘‘beneath’’’] the NQ qualifiers.  That is, each NQ qualifier is an «aufheben» determinate negation / conservation / elevation-into-one-step-higher-generality of an individual N quantifier. 

The joint «aufheben» elevation of the quantitative ordinals «species» yields the «genos»q’, of the qualitative ordinals.

For this first layer of interpretation of these purely-qualitative NQ meta-numbers -- which does not yet make explicit their universal interpretability for the modeling of dialectical progressions -- this is all that they represent:  abstract temporality; [abstract chronological] order; generic ordered-ness; the consecutive succession of qualitative ordinality; the consecuum of order quality or of order qualities.

But even here, at this minimally-interpreted stage of the construction of the NQ dialectical arithmetic, there is already a kind of generic connotative entailment at work.  True, it is but a shadow, and but a ‘pre-vestigial’ harbinger, of the richness of the kind of particularity of categorial followership that drives forward, intuitively, the dialectical, purely-qualitative logic of the more concrete, more specific dialectical-algebraic interpretations thereof.  A case in point is exemplified in the very NQ algebraic model of The Dialectic of Nature that is used for the illustrations presented herein.

This generic connotative entailmentcan be formulated as follows:  second-ness’ follows -- and even follows from --first-ness’; third-ness’ follows [from] second-ness’, and so on.

In the next section, the construction, by iterated interpretations layering, of the Seldonian first dialectical arithmetic will advance from this harbinger of connotative entailment to the following, still generic, but at last also explicitly dialectical, form of connotative entailment ordinality:   first full antithesis follows from the self-interaction of [«arché»-]thesis; first full synthesis follows from the mutual interaction of first full thesis and first full antithesis’,    and so on.

III.  Dyadic Seldon Function Interpretation of the Initial Generic NQ Ontological Category Qualifiers. 

dialectical model meta-equation form for the functions-family of the Seldon Functions is that of a generic cumulum symbol [ ‘|-|-|’ ] on the LHS [Left-Hand Side] of  the dialectical meta-equation, equated to an RHS expression representing self-reflexive operation of an [«arché», ‘‘‘seed’’’, ‘‘‘cell-form’’’, or ultimate ancestor ontological category symbol [represented, generically, by ‘q1’] -- indicating its recurring self-reflexionvia a meta-exponentiated’, monotonically increasing whole-number-valued ‘‘‘independent variable’’’ [‘h ] -- on the RHS of the generic Seldon Function equation, viz. [with generic-ness’ connoted by the “rectangular” motif of the symbols-set]:

|-|-|h      =      | q1 |vh, for h in { 0, 1, 2, 3, . . . }, v in {2, 3}.                        

If v = 2, the Generic Seldon Function above is said to belong to the Dyadic Seldon Function sub-family.  If v = 3, the Generic Seldon Function above is said to belong to the Triadic Seldon Function sub-family.  Our remarks herein are concentrated on the Dyadic Seldon Functions, because the main dialectical-mathematical meta-equation’, modeling a historical dialectic, exposited herein, is of the v = 2 variety.

With v = 2, and selecting that special generic Dyadic Seldon Function form that we reserve for a historical dialectic, the form of the meta-model meta-equation to be used in the illustrations herein, becomes, more specifically --

>-|-<t­     =        < qa >2t ­, for t in { 0, 1, 2, 3, . . . }.                      

-- wherein the symbol t, replacing the more generic symbol h, represents the generic algebraic parameter-variable for the historical epoch modeled, and wherein, in general, the “angular” motif of the entire symbols-set used is to connote the historical dialectic domain of dialectical modeling.
The Seldon Functions bring with them a further, second layer of interpretation of the NQ qualifiers,  

{ q1, q2, q3, ... }

by which they are interpreted as qualifiers that stand for generic dialectical physio-ontological categories, e.g., for ‘‘‘physis’’’ categories, or for full or partial meta-physis categories, or for full or partial uni-physis categories.

If we assign [ [---> ] the «arché»-physis category, qa, to the generic NQ qualifier meta-number, q1, as signed by ‘qa [---> q1’, and if we can discern that qa, and all of its successor-categories, and their cumula, as generated by its successive, cumulative, ‘Seldon-functional self-operations’, connote «aufheben» operators, that is, dialectical negation operators, then the Dyadic Seldon Function is seen to signify, under the axioms of the system of arithmetic of the NQ meta-numbers[ http://www.dialectics.org/dialectics/Correspondence_files/Letter17-06JUN2009.pdf ], a self-iterated, cumulative recurrence of dialecticalnegations of [the] negations.

With every [unit] increase in t, the Dyadic Seldon Function ‘formulaic recipe’ calls for the dyadic self-operation of the result of the previous dyadic self-operation, i.e., for a negation of the negation of the result of the previous negation of the negation.  Only for t = 0 -- only for the case in which no self-operation occurs -- is the “result” a singleton [physio-] ontological category symbol, the symbol for the «arché» [physio-]ontological category alone, instead of that “result” taking the form of a cumulum of [powers-of-]two [or more] such symbols, i.e., a “non-amalgamative sum” [cf. Musès], or an  «a-sumbletoi» sum [cf. Plato], of ‘[physio-]ontological category symbols, since 20 =  1, and since qa1 =  qa.

>-|-<0     =   < qa >20    =   < qa >1   =        

< qa >     =     qa.

For example, if we take epoch t = 1, and denote the «arché» ontological category simply by a, for syntactical convenience, then the Dyadic Seldon Function calls for the following, as per the NQ_ axioms, since 21 =  2 --

 >-|-<1   =    < a >21      =       < a >2      =        

< a > x < a >      =     a  x  b.

-- wherein a [---> q1 connotes the «arché» category, or ‘‘‘«arché»-physis’’’, and where 

 b [---> q2 

 connotes the first meta-physis category, with ‘+’ here standing for a generalized addition operation, that encompasses the addition of qualitatively distinct terms, and with ‘´’ here standing for a generalized multiplication operation, that encompasses the multiplication operation specific to the NQ qualifiers.

If we take 

< a > x < a >’ 


< a > 

 connoting the category to be dialectically negated, and with 

< a >  

connoting the category doing that dialectical [self-]negating, with 

< a >’ 

as the dialectical, determinate negation-sign’ specific to  

< a >  

as the object of the so-indicated dialectical, determinate negation operation, then we have 

< a > x < a >’, 

as a whole, as connoting the first dialectical negation, by the negation-operation  

< a >

 of the self-same negation operation,  

< a >, 

that is also the operand of the negation-operator  

< a >

forming what Seldon calls an -- ideographically signed -- 

‘subject [< a >]-verb[< a >]-object[< a >] identical’, 

yielding a first dyad:  ‘‘‘physis + meta-physis’’’, or

«arché» category  +  first meta-category’, viz. --

< a > x < a >    =    qa   x   qaa    =     

qa   x   qb  =      

a  +  b  

-- which, in terms of the generic, minimally-interpreted NQ arithmetic, is a dialectical interpretation of the generic --

|-|-|1     =     |[ q1 ]|21   =      |[ q1 ]|2   =     |[ q1 ]|  |x|  |[ q1 ]|    =   |[ q1  |+|   q1+1 ]|    

q1  |+|   q2.

The second iteration of this dialectical negation of the negation, corresponding to the consecutively next value of t namely, t = 2, for the NQ_  arithmetic interpreted for [psycho]historical dialectics, yields the following, ontologically-expanded cumulum of ontological categories -- a dyad of dyads, consisting of 4 consecutive ontological categories:

>-|-<2     =    < a >22   =   < a >4    =

< < a >2 >2    =    < a  +  b >2           

=    < a  +  b > x < a  +  b >

=     a  +  b  +  c  +  d.

The additional 2 ontological category-symbols above are dialectically interpreted, per the E.D. standard, as follows:

c  =  third ontological category, first full uni-physis category;
d  =  fourth ontological category, second meta-physis category.   

We will not here pursue this E.D. standard dialectical interpretation of the ontological categories generated by the generic Dyadic Seldon Function beyond epoch t = 2, as they are not required for the purposes of this vignette.

The purely-qualitative calculations illustrated above describe our expectations as to the meaning of this vignette’s illustrative meta-modelin terms of generic characterizations of its successive, consecutive dialectical categories. 

The next section addresses the heart of this meta-model -- the specific meanings of the generic dialectical categories as applied to the ‘‘‘special case’’’ of The Dialectic of Nature in general.

IV.  ‘‘Self-Activity’’’ and ‘‘Self-Change’’’ as Captured in the Dyadic Seldon Functions of the NQ_ Arithmetic. 
If we would extend the theory left to us by Marx and Engels, of the dialectic of human history -- the dialectic of human Nature, i.e., the dialectic of just the human part of Nature -- explicitly into a theory of The Dialectic of Nature as a whole -- as begun by Engels, in his posthumously published, incomplete, and fragmentary manuscript, given the title posthumous Dialectics of Nature -- then we must extend the Marxian concepts of self-activity and of self-change, as set forth by Marx and Engels in the passages quoted in section I., above, to encompass selves, i.e., “subjects”, or causal agents, other than individual human “subjects” / agents, or human-social, collective “subjects” / agents -- whole human societies as collective “subjects” / agents -- alone.  In framing a Marxian theory of The Dialectic of Nature as a whole, we must get beyond limiting our discourse of ‘subject-ivity’, of ‘subject-ness’, of ‘subject-hood’ -- i.e., of the «genos» of causal agency in general -- of an agent that operates upon natural objects, including upon the objective aspects of its own self, to just one of the «species» of that «genos»; indeed, beyond limiting our discourse to just the most recent and most developed, self-conscious «species» of that «genos» known to us:  humansubject-ivity’.

Causal agency, in this cosmos, is not limited to human agency -- far from it!

Therefore, the quality of ‘subject-ivity’, ‘subject-ness’, ‘subject-hood’ is not limited to human individuals or to whole human societies, although human ‘subject-ivity’ or agency is the highest degree of ‘subject-ivity’ known to humans.

Any natural causal agent whose name can aptly -- i.e., with empirical truthfulness -- be cast into the “subject” role and position / “slot” of a well-formed English sentence is a “subjectof some degree.  A special case of such sentences involves the same name occurring, aptly, in both the subject and the object “slots” of such a sentence -- forming a ‘‘‘subject / object identical’’’, or, in our cases, a ‘subject / verb / object identical’, since the entity whose name is both subject and object of such a sentence also has its [self-]activity, its “verb”, absorbed into itself, absorbed into that entity, and one with that entity.  That is, such an entity is thereby being represented as an ‘event-entity’, an ‘‘‘eventity’’’, or, in mathematical terms, as an ‘‘‘operator’’’, unifying both “operation” and “operand” -- and thus also as a ‘noun / verb identical’; as an ‘operation / operand identical’, or as a ‘function / argument identical’.

We illustrate, below, the ways in which a Dyadic Seldon Function Historical-Dialectical Meta-Equation Meta-Model describes a given history as a self-progression of self-activity for a thereby self-growing [via [past] self-activity]] cumulum of self-actors / ‘‘‘eventities’’’, yielding an ontologically different, self-«aufheben» self-expanded self-acting cumulum, for each of its successive historical epochs -- i.e., for each successive value of the discrete time parameter, t. We so illustrate by means of the special case of the most general Dyadic Seldon FunctionMeta-Model available -- the Dialectical Theory of Everything, Dialectic of Nature as Totality Meta-Equation --

>-|-<t­     =     < n >2t ­

-- with n denoting the «arché-physis» ‘physio-ontological’ category of ‘sub-nuclear particles”, e.g., quarks and leptons.

Epoch t          Cumulum-form             Power-form         tth ‘Subject-[Verb[ x ]-]Object-Identical   Product- / Result-form
t = 0:       >-|-<0  = < n >20  = < n >            = < n >

t = 1:       >-|-<1  = < n >21  = < n >x< n >       = < n + s >

t = 2:       >-|-<2  = < n >22  = < n  +  s >< n  +  s > = < n + s + qsn + a >

t = 3:       >-|-<3  = < n >23  = < n + s + qsn + a >< n + s + qsn + a >   =   

                                                             < n + s + qsn + a + qan + qas + qasn + m >
. . .

In the table above, the symbol s stands for the first meta-«physis» ‘physio-ontological’ category of ‘sub-atomic particles”, that is, of ‘meta-quarks’, e.g., protons and mesons.  The symbol a stands for the second meta-«physis» ‘physio-ontological’ category, of ‘atomic nuclei”, that is, of ‘meta-sub-atomic 

particles’, e.g., Helium nuclei, He++.  The symbol m stands for the third meta-«physis» category 

of ‘physio-ontology’, that of ‘molecules”, i.e., of ‘meta-atoms’, e.g., H2O, water.  The foregoing list covers the self-hybrid categories of ‘physio-ontology’ expressed in the table above.  We need not address the symbols for the merely hybrid categories of ‘physio-ontology’, such as qsn and qasn, or their meanings, within the purposes of this vignette. 

For all epochs t > 1, each of the entries under the ‘tth ‘Subject-[Verb[ ´ ]-]Object-Identical’ column in the table above can be characterized in all of the following ways --

1.  A ‘‘‘self-activity’’’; an activity of / by a [pre-human] ‘‘‘self’’’ / “subject” / causal agency [back-]upon that same ‘‘‘self’’’ / “subject” / causal agency, thus also functioning as “object” thereof -- as also object of / to itself.

2.  A ‘‘‘self-activity’’’; a ‘‘‘self-action’’’, causing ‘‘‘self-change’’’-- here, not merely quantitative change, but qualitative change, ontological change [expansion of the cumulum of possible ontology] -- self-induced change; change-in-self, induced by self.

3.  A self-labor [in a pre-human sense of the word “labor”]; a labor upon self by self; a work upon self by self; a ‘self-working-up’.

4.  A self-re-flex-ive function [cf. Russell,; Wittgenstein]; a function which can be characterized [-ive] as, bending [flex] back [re-] upon, or to impact, the very source [self-] which generated / generates that function.

5.  A self-re-flux-ive function [cf. Ancient Eastern Philosophies / Religions]; a ‘‘‘karmic’’’ action which is characterized [-ive] as, flowing [flux] back [re-] upon, and thus impacting, the very source [self-] which generated / generates that action[cf. “the karma-yoga performed by all things”].

6.  An «autokinesis» [cf. Plato, Ancient Western Philosophy]; a self-motion; a self-movement; a self-change; a change-in-self, induced by self.

7.  A concrete, material self-mirroring / ‘‘‘self-reflection’’’ / self-beholding that irrupts new ontology -- that surges-up a new, expanded ‘cumulum of ontology possibility’ as expanded cosmological ‘self’[cf. Hegel, ‘‘‘Being-for-self’’’].

8.  [from t = 2 on]:  A re-squaring of the already squared; a re-self-negating / determinate-negating / self-changing of the already self-negated / determinate-negated / self-changed.

9.  A [quadratically]nonlinear term [as long as any of the terms in the ‘cumulum’ sum-representations being ‘‘‘multiplied’’’ together are ‘‘‘unsolved-for’’’ / ‘unsemantified’, ‘dialectical-algebraic’ unknowns].

Links to definitions of additional Encyclopedia Dialectica special terms deployed in the discourse above --

«arithmos aisthetos»

«arithmos eidetikos»





dialectical categorial progressions

homeomorphic defects of models

[The] Human Phenome


immanent critique


ontological category





self-meta-monad-ization or self-meta-individual-izationor self-meta-holon-ization